Topics from the Theory of Numbers

• Introduction, Historical Background, and Notations.- and Historical Background.- Introductory Remarks and Notations.- Elementary Number Theory.- Divisibility.- Congruences.- Quadratic Residues.- Arithmetical Functions.- The Theory of Partitions.- Topics from Analytic and Algebraic Number Theory.- The Distribution of Primes and the Riemann Zeta Function.- The Prime Number Theorem.- The Arithmetic of Number Fields.- Ideal Theory.- Primes in Arithmetic Progressions.- Diophantine Equations.- Fermat’s Equation.

From the reviews:"When one has the opportunity to teach an undergraduate course on the subject there are plenty of excellent books to choose from. Depending on the approach, one may choose...a classical text that brims with elegance in the choice of topics or proofs that will leave our students avid for more. The book under review falls [into] this category, but also has plenty of well-chosen exercises at the end of every chapter. This is a book written with love for the subject and with the presence of its readers (students) in mind all the time."   —MAA Reviews (Review of Second Edition, Softcover Reprint)“In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald.”   —Marc Kac (Review of Second Edition)“For the second edition the author has made several changes, mainly in the third part of the book concerning analytic and algebraic number theory. There is an entirely new chapter on $L$-functions and primes in arithmetic progressions, another new chapter on the arithmetic of number fields, and a largely rewritten chapter on Diophantine equations...The revisions have undoubtedly increased the value of this textbook, and the reviewer does not hesitate to recommend the volume for anybody interested in number theory. Among the many merits of the book one should mention the author’s lively and stimulating style of writing as well as the carefully chosen exercises at the ends of the chapters.”   —Mathematical Reviews  (Review of Second Edition)“This book is designed for use in a first course in number theory at the junior or senior level...The author has certainly planned his bookwell, chosen material that will be stimulating to its intended audience, and carried the project through in such a way that interest seldom flags.”   —Mathematical Reviews (Review of First Edition)